Any engineering major is as good as any other if you are on a NROTC scholarship already. If you are not on scholarship and want to switch to the NUPOC program, which does pay a scholarship, a nuclear engineering major will help. If you are going to pay your way though college on your own dime you might as well become an officer. For enlisted you could finish your degree while you are in then get a masters on the GI Bill after the Navy.
For an officer " working on the nuclear propulsion aspects " you are not working on anything directly your hands never touch the controls. If you want to become a nuclear reactor operator you need to be an ETN, an enlisted, nuclear-trained electronics technician. My son happens to be one of those, on an attack submarine. If you plan to make a lifelong career of the Navy the officer route is a better choice, who knows, you might make admiral someday. However if you are planning to do a stint in the Navy and move into the civilian job market while you still have your youth, enlisted is still a better plan. There are plenty of ex-officers working for ex-enlisted Navy nukes in the civilian world.
Since you are talking about the "engineering section" of a ship and by the Navy's own terminology nukes are an "engineering" rating category, I am not doing to split hairs over terminology of that versus an "engineering degree" from a civilian college. But the job of an enlisted reactor operator, an ETN, is to actually operate the controls of the nuclear reactor that controls the nuclear reaction, as well as to troubleshoot and repair control systems (electronic circuitry, fiber optics, and the like). An engineering officer gives the orders. However an enlisted person can also become an "engineering officer of the watch" EOOW just like an officer can, and can become engineering watch supervisor "EWS" also.
The Nuclear Power School for officers is more theory based and goes deeper into calculus than the enlisted school, however both officers and enlisted must graduate Nuclear Power School (6 months) and prototype (6 months).
My son likes his job very much and enjoys being on the crew of a brand new attack submarine. People who are not going to like nuke because it is too much work, are apt to shirk work wherever they find it and cut corners when they do work. That is one reason why ex-nukes are so highly regarded in the civilian world.